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3 May 2011
CHAPTER 12: MORE REALISTIC AND COMPLEX PRICING 135
I.
INTRODUCTION
This is Luke Froeb, author of Managerial Economics: a problem-solving approach, and this short video is
designed to accompany chapter 12, “More Realistic and Complex Priciing.”
National Retail Price and Quantity Series
2.00
4,000
1.90
3,500
1.80
3,000
1.70
$/Lb.
1.50
2,000
1.40
Lbs.
2,500
1.60
1,500
1.30
1,000
1.20
500
1.10
1.00
0
Month
Retail Price
Retail Quantity
In the chart above, we see the national price and quantity series for a category of frozen food called
“frozen pies.” These include carrot cake, pumpkin pie, and apple pie, sold in the freezer section of
grocery stores. The salient feature of the data are the big seasonal spikes in quantity, plotted in blue,
and the big seasonal dips in price, plotted in pink, that occur at the same time. In November and
December of each year, average price declines by about 30% and quantity increases by several hundred
percent.
Now, if you remember the lessons of chapter eight, you might be tempted to jump to the conclusion
that this chart simply represents the normal movement along a demand curve: as price falls, quantity
increases, and the price elasticity of demand looks to be about -10. But this explanation does not
explain why price suddenly decreases during the two months right before Christmas?
Something is causing the manufacturers to reduce price right before the big seasonal peaks in demand.
In this chapter, we move beyond the simple pricing model introduced in chapter 6 to more “complex
and realistic” settings. In this short video, we will cover pricing of multiple products, revenue
management, and promotional pricing. And at the end, I will clear up the mystery of the big seasonal
dips in pricing.
I.
PRICING COMMONLY OWNED PRODUCTS
In chapter six we showed you how to choose the best price using marginal analysis.

If MR>MC, then sell more, and you do this by decreasing price.

But if MR<MC, then sell less, and you do this by increasing price.

When MR=MC, price is set optimally.
This advice is derived from a very simple setting: a single firm setting price on a single product. In this
section we extend the analysis to cover the more realistic setting of a single firm setting prices on
several commonly owned products.
To get the basic idea, it helps to start with a concrete example: let’s look at the 2008 acquisition of
Anheuser-Busch by Imbev. Imbev owned Labatts and was acquiring the beer brands of Anheuser,
including Budweiser. In upstate New York, Labatts and Budweiser are the two strongest brands, and the
Antitrust Division of the US Department of Justice made Imbev divest the Labatts brand before they
would let the merger proceed. Why did they do this?
Here is the logic. Before the merger, each brand is priced independently. Each firm weighs the benefits
of a price increase—a higher margin--against the costs of a price increase, lower sales. Each firm
chooses a price where MR=MC.
But after the merger, this simple profit calculus changes. Now the costs of a price increase are reduced
because some of the lost sales will be picked up by the newly acquired product. So, post-merger, price
goes up, and the size of the price increase depends on the strength of the substitution between the two
merging brands.
Mathematically, a merger or acquisition reduces MR because some of what you gain by increasing
output comes at the expense of your newly acquired product. As MR falls below MC, the merged firm
reduces output, which it does by increasing price on both products
[GRAPHIC SHOWING MR=MC, then MR FALLING BELOW MC—make it go down vertically, AND THE FIRM
RAISING PRICE IN RESPONSE, which increases MR back up to equality].
The Department of Justice used this logic to predict that the transaction, as originally proposed, would
likely have led to higher prices for beer in upstate N.Y. By requiring the divestiture, the Department of
Justice made sure the Labatts and Budweiser would still be independently priced; so price would not go
up due to the merger.
II. REVENUE MANAGEMENT
To make this example concrete, imagine that you are a parking lot developer, deciding how many spaces
to build onto a particular property. You should immediately recognize this as an extent decision, from
chapter four, and use marginal analysis to decide “how many” parking places to build. Marginal analysis
tells you to keep adding spaces as long as the benefits of adding a space--the long run MR—are bigger
than the costs of adding spaces--the long run MC.
But once you build the lot, you then have to determine what price to charge at the lot. This is a
different decision, and requires a different profit calculus. Since the costs of building parking spaces do
not vary with the decision of how many to sell, you ignore these costs, lest you commit the fixed cost
fallacy.
Instead, you keep selling lots as long as short run MR>short run MC. Because of the big fixed costs, and
small marginal costs, it is likely that you will hit the capacity of the lot before MR falls down to MC.
If, at the capacity of the lot MR>MC, then you want to price to fill the lot, and this is called “revenue
management.”
The only difficult part of revenue management is figuring out which price matches expected demand to
capacity. For parking lots, this is relatively easy because you get to “see” demand every day. If the lot is
filled before 9am in the morning, you should raise the price; and if it is empty at 9am each morning then
you should lower the price. Aim for a price where the lot is filled at 9am each day.
Revenue management gets difficult when it is hard to predict what demand will be. For many
applications, like cruise lines, demand varies from year to year or from trip to trip, so predicting which
price will fill capacity is very difficult. When there is uncertainty about which price to charge, you want
to set a price that minimizes the “error costs” of mis pricing.
A price too high means unused capacity; but a price too low means foregone income-- you could have
raised price on all the capacity you did sell.
In the graphic on the screen, we illustrate the effects of uncertainty about demand by imagining that
demand could turn out to be high, or low. Expected demand is denoted by a dashed line and is the
average of the high and low demands. The price that matches expected demand to capacity is denoted
on the screen. However, at this price, demand will be either high, and you could have raised profit by
charging more; or demand is low, and you could have raised profit by charging less.
INSERT GRAPHIC OF TWO ERROR TYPES <<CALL ME IF THIS IS UNCLEAR>>: Have a downward sloping
demand curve that is uncertain, i.e., it could be high or low. Denote this by moving demand up and
down. THEN FIX THE EXPECTED DEMAND (make it a dashed line) at the average of the high or low
demands, and draw a vertical line on the horizontal (quantity) axis denoting the “capacity.” Draw a
horizontal line from the intersection of expected demand curve and capacity to the vertical price axis to
figure out which price matches expected demand to capacity. THEN, show that under high demand this
price is too low (you could have raised price and earned more money) (UNDER-PRICING ERROR). AND
AT LOW DEMAND YOU HAVE UNUSED CAPACITY (OVER-PRICING ERRO)
An optimal pricing mechanism minimizes the expected costs of these two pricing errors. For example, if
the costs of over-pricing are bigger than the costs of under-pricing, then you shade price down a little bit
to avoid over-pricing. Conversely, if the under-pricing errors are more costly, then you want to price
slightly higher, to avoid under-pricing.
III. PRICING WITH PROMOTION AND ADVERTISING
The final topic of this video is pricing with promotion and advertising. In your marketing class,
“advertising” is generally thought to increase demand for a product by “brand building,” by for example
getting a celebrity endorsement, or associating the product with a certain type of lifestyle or quality.
<<MIGHT WANT TO INCLUDE AN ADVERTISEMENT FROM A MAGAZINE HERE SHOWING AN SUV AND
YOUNG PEOPLE GOING TO THE BEACH OR MOUNTAINS>>. Economists model advertising as making
demand for the product less elastic, so you would expect that this kind of advertising to lead to higher
prices.
In your marketing class, “promotion” refers to short term tactics designed to increase sales, like end-ofaisle displays in the grocery store, or coupons in the newspaper. <<MIGHT WANT TO INCLUDE AN
PROMOTION FROM AN IN-STORE CIRCULAR OR A COUPON-BASED ADVERTISEMENT HERE>>.
Economists model promotion as making demand for the product more elastic, so you would expect this
kind of advertising to result in a lower price
1.10
1.00
Relative Price
0.90
0.80
0.70
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0
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Relative Quantity
No Promotion
Display Only
Feature Only
Feature & Display
In fact, that is what we see. I have estimated demand for super-premium ice cream--so named because
it has a high percentage of butterfat which makes it taste really good, but which is also really bad for
you. In the figure on the screen, I plot the four demand curves for one of the brands, at the prices at
which it is sold. The curve on the far left is the least elastic or steepest of the four demand curves. It
also has the highest price. This demand corresponds to no promotional activity.
The curve on the far right has the flattest, or most elastic demand. It corresponds to the highest levels
of promotional activity. You can also see that during these high promotional periods, price was the
lowest. The other two demand curves have intermediate levels of promotional activity, and
intermediate levels of price.
Promotional activity makes demand more elastic, probably because it makes consumers more aware of
price differences. And if you make them more aware of price differences, it also means that they react
more to a the difference. When you promote a product, it makes sense to reduce its price.
We are now in a position to try to figure out why firms reduce price on frozen pies in the two months
leading up to the holiday season. Given what we have just discussed about elasticity, it is reasonable to
guess that demand for frozen pies gets much more elastic during this period. This is due to two factors.
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First, they are promoted more heavily during this period. And as you promote the product, demand
becomes more elastic, so it makes sense to also reduce price. But there is a second factor at work as
well. During the holiday season, a lot of people buy items, like pumpkin pie, that they don’t buy at any
other time of the year. Economists have found that these consumers are more price elastic than
consumers who buy the product all year, so holiday demand becomes more elastic, on average. Firms
rationally respond by reducing price.